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Pattern
A pattern is a form, template, or model (or, more abstractly, a set of rules) which can be used to make or to generate things or parts of a thing, especially if the things that are generated have enough in common for the underlying pattern to be inferred or discerned, in which case the things are said to exhibit the pattern. Pattern matching is the act of checking for the presence of the constituents of a pattern. The detection of underlying patterns is called pattern recognition. The question of how patterns arise naturally is dealt with by the scientific field of pattern formation. Some patterns (for example, many visual patterns) may be directly observable through the senses. Some patterns are named. Simple decorative examples are stripes and zigzags. Further examples include the regular tiling of a plane, echoes, and balanced binary branching. The simplest patterns are based on repetition/periodicity: several copies of a single template are combined without modification. For example, in aviation, a "holding pattern" is a flight path which can be repeated until the aircraft has been granted clearance for landing. Pattern recognition is more complex when templates are used to generate variants. For example, in English, sentences often follow the "N-VP" (noun - verb phrase) pattern, but some knowledge of the English language is required to detect the pattern. Pattern recognition is studied in many fields, including psychology, ethology, and computer Science. In addition to static patterns, there may be patterns of movement such as oscillation. Nature The planets of our solar system are caught in an incredibly ancient pattern by the gravity of the Sun. The planets have been following their (very predictable) elliptical orbits for billions and billions of years. There is certainly a recognizable pattern/cycle there. * Sea shells, Sand Dollars * Sand dunes, Grand Canyon * Tree branches, ferns, coastal lines, clouds * Fir waves and tiger bush are examples of patterned vegetation * Snowflakes Golden Ratio A reoccurring theme found in the biology of nature is the golden ratio. The golden ratio is a+b to a is as a is to b. It has a direct relationship to the Fibonnacci numbers. This pattern was exploited by Leonardo da Vinci in his art. The Fibonacci pattern has a closed-form expression. These patterns can be seen in nature, from the spirals of flowers to the symmetry of the human body (as expressed in Da Vinci's Vitruvian Man, one of the most referenced and reproduced works of art today. Art * Modern art: Mondrian, Op Art * Impressionism: Pointillism * Performance Art: Crop circles * Music: Minimalism Science and mathematics Fractals are mathematical patterns. Naturally occurring patterns obey certain principles also found in fractals, for example self-similarity. Even though self-similarity in nature is only approximate and stochastic, integral measures describing fractal properties can also be applied to natural "fractals" like coastal lines, tree shapes, etc. (see fractal geometry). While the outer appearance of self-similar patterns can be quite complex, the rules needed to describe or produce their formation can be extremely simple (e.g. Lindenmayer systems for the description of tree shapes). Patterns are also common in other areas of mathematics. Recurring decimals will repeat a sequence of digits an infinite number of times. For example, 1 divided by 81 will result in the answer 0.012345679... the numbers 0-9 (except 8) will repeat forever — 1/81 is a recurring decimal. A reoccurring pattern is on of the 5 cornerstones of the definition of a mineral in geology. A mineral must show it's elements in a three-dimensional reoccurring pattern (aka a crystal matrix). * Crystals * Tessellation * Penrose tilings * Cellular Automata * Mineral Computer Science * Pattern matching * Design patterns * Regular expressions Patterns in Pedagogics * Pedagogical patterns Quotation :"A pattern has an integrity independent of the medium by virtue of which you have received the information that it exists. Each of the chemical elements is a pattern integrity. Each individual is a pattern integrity. The pattern integrity of the human individual is evolutionary and not static." R. Buckminster Fuller (1895-1983), U.S.American philosopher and inventor. Critical Path, 1981. :"Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern." Alfred North Whitehead (1861-1947), English philosopher and mathematician. Dialogues, June 10, 1943. Mathematics is commonly described as the "Science of Pattern." See also * Pattern recognition * DNA motifs * Pattern (sewing) * Form constant * Automated pattern digitizing * A Pattern Language * Fibonacci Number External links * Geometric Arts * Pumpkin Carving Patterns Category:Perception :de:Muster (Struktur) :fa:الگو :nl:Patroon (vorm) :ja:パターン :vi:Mẫu (dạng thức) :sh:Uzor